SOPHE grid implementation differs from EASYSPIN

[abehersan]

Hi!

It seems to me that the implementation of the SOPHE grid given in

DeerLab/deerlab/utils.py

Line 787 in b9b76e4

def sophegrid(octants,maxphi,size):

differs from that given in EASYSPIN, see
https://github.com/StollLab/EasySpin/blob/5c396b941b9216377d8507a0187ef378dfaeaf35/easyspin/sphgrid.m#L44C30-L44C30

I implemented the SOPHE grid just as is done in EASYSPIN in Julia and I noticed the following differences with the Python implementation.

• The weights of the points in the grid are bunched towards the XZ plane rather than towards the pole of the sphere
• The density and sparsity of points close to the XZ plane is much less homogeneous than for the rest of the octant

All calculations are done for one octant, a maximum phi of pi/2 and 100 points in theta. Left is Python, right is EASYSPIN in Julia. The colormap maps to the weight of the point. The sum of weights does add up to 4pi.

It is not 100% obvious to me what the difference could be between implementations since the source for both seems equivalent. Still I thought it was useful to shine light on this.

Best wishes,
Abraham

[abehersan]

I must note that I commented out

DeerLab/deerlab/utils.py

Line 899 in b9b76e4

weights = weights/np.sum(weights)

In order to have weights normalized to 4pi.

For completeness here are the test functions I wrote that generate the plots above:

Python:

def SOPHE_test():
    import mpl_toolkits.mplot3d as mplot3d
    import matplotlib.pyplot as plt

    def cart_coords(theta, phi, r=1):
        return r * np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)])

    theta, phi, wght = SOPHE_grid(octants=1, maxphi=np.pi/2, size=100)
    print(sum(wght))
    [xs, ys, zs] = cart_coords(theta, phi, r=1)

    fig3d = plt.figure(figsize=(11.3, 8.7))
    subplot3d = fig3d.add_subplot(111, projection="3d")

    subplot3d.set_xlabel("X")
    subplot3d.set_ylabel("Y")
    subplot3d.set_zlabel("Z")

    p = subplot3d.scatter(xs, ys, zs, c=wght.T)
    fig3d.colorbar(p, ax=subplot3d)
    plt.tight_layout()
    plt.show()

    return

Julia

using GLMakie

function SOPHE_test()
    theta, phi, wght = sphgrid(1, pi/2, 100, true)
    println(sum(wght))
    fig = Figure()
    ax, mesh = meshscatter(fig[1, 1],
        sin.(theta) .* cos.(phi),
        sin.(theta) .* sin.(phi),
        cos.(theta), color=wght, markersize=0.01)
    Colorbar(fig[1,2], mesh)
    fig
end

[HKaras]

Many thanks for highlighting this issue. It is indeed a bug caused classic zero vs one starting array positon. I have fixed this is pull request #464

[HKaras]

Issue fixed in #464